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Mid-Course Guidance Law for Long Range Multi-Purpose Missiles
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作者 罗喜霜 张天桥 《Journal of Beijing Institute of Technology》 EI CAS 2002年第2期121-124,共4页
A useful mid course guidance law for long range multi purpose missiles is proposed. The law consists of two parts. One is used in the horizontal guidance plane, and the other in the vertical guidance plane. The mid ... A useful mid course guidance law for long range multi purpose missiles is proposed. The law consists of two parts. One is used in the horizontal guidance plane, and the other in the vertical guidance plane. The mid course is combined with variable structure proportional navigation in the homing phase. Simulation results show that the proposed guidance law can meet the demands for starting up the homing phase and so the handing over between mid course guidance and terminal guidance can be carried out successfully. 展开更多
关键词 multi purpose missile mid course guidance demands for startup
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Kill probability modeling of multi-purpose guided missile against gunship and its application
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作者 DU Zheng CHEN Wan-chun 《Journal of Measurement Science and Instrumentation》 CAS 2014年第2期9-18,共10页
Aimed at current deficiencies of multi-purpose guided missile kill probability model against gunship, the concept of the important coefficient of vulnerability blade unit is proposed in this paper. Laser fuze actuatio... Aimed at current deficiencies of multi-purpose guided missile kill probability model against gunship, the concept of the important coefficient of vulnerability blade unit is proposed in this paper. Laser fuze actuation model and warhead condition kill probability model of rotor blades are established by Monte Carlo method and kinetics theory with new ideas. Based on limited data, armor thickness of gunship is estimated, and a complete multi-purpose guided missile kill probability mathematical model is established, which provides necessary mathematical tool for the accurate and objective analysis of multi-purpose guided missile kill probability against gunship. Based on the establishment of the model, sensitivity analysis and optimal design of the main factors of multi-purpose guided missile kill probability are conducted, and the results show that the single multi-purpose guided missile lethality performance can be improved significantly by sensitivity analysis and optimization. 展开更多
关键词 multi-purpose guided missile gunship rotor blade the important coefficient of vulnerability blade unit armorthickness kill probability
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Random walk dispersion model for missile contrail particles in cross-airspace environments
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作者 Chenshuo Li Debin Fu Tianyu Wei 《Defence Technology(防务技术)》 2025年第7期307-320,共14页
Missiles provide long-range precision strike capabilities and have become a cornerstone of modern warfare.The contrail clouds formed by missile during their active flight phase present significant chal-lenges to high-... Missiles provide long-range precision strike capabilities and have become a cornerstone of modern warfare.The contrail clouds formed by missile during their active flight phase present significant chal-lenges to high-altitude environmental observation and target detection and tracking.Existing studies primarily focus on specific airspace regions,leaving critical gaps in understanding the effects of long dispersion times,wide altitude ranges,and variable atmospheric conditions on missile contrail clouds.To address these gaps,this article develops a numerical method based on the Lagrangian random walk model,which incorporates various velocity variation terms,including particle velocity caused by the difference of wind field,by the thermal motion of local gas molecules and by random collisions between contrail cloud particles to capture the influence of environmental wind fields,atmospheric conditions,and particle concentrations on the motion of contrail cloud particles.A general coordinate system aligned with the missile's flight trajectory is employed to represent particle distribution characteristics.The proposed method is in good agreement with the conducted experiments as well as with the available numerical simulations.The results demonstrate that the proposed model effectively simulates the dispersion state of contrail clouds,accurately reflecting the impact of large-scale wind field variations and altitude changes with high computational efficiency.Additionally,simulation results indicate that the increased distance between gas molecules in rarefied environments facilitates enhanced particle dispersion,while larger particles exhibit a faster dispersion rate due to their greater mass. 展开更多
关键词 missile contrail Dispersion process Random walk model Concentration distribution Cross-airspace
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Time-efficient cooperative attack strategy considering collision avoidance for missile swarm
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作者 HU Yixin XU Yun DANG Zhaohui 《Journal of Systems Engineering and Electronics》 2025年第5期1306-1316,共11页
In the realm of missile defense systems,the self-sufficient maneuver capacity of missile swarms is pivotal for their survival.Through the analysis of the missile dynamics model,a time-efficient cooperative attack stra... In the realm of missile defense systems,the self-sufficient maneuver capacity of missile swarms is pivotal for their survival.Through the analysis of the missile dynamics model,a time-efficient cooperative attack strategy for missile swarm is proposed.Based on the distribution of the attackers and defenders,the collision avoidance against the defenders is considered during the attack process.By analyzing the geometric relationship between the relative velocity vector and relative position vector of the attackers and defenders,the collision avoidance constrains of attacking swarm are redefined.The key point is on adjusting the relative velocity vectors to fall outside the collision cone.This work facilitates high-precision attack toward the target while keeping safe missing distance between other attackers during collision avoidance process.By leveraging an innovative repulsion artificial function,a time-efficient cooperative attack strategy for missile swarm is obtained.Through rigorous simulation,the effectiveness of this cooperative attack strategy is substantiated.Furthermore,by employing Monte Carlo simulation,the success rate of the cooperative attack strategy is assessesed and the optimal configuration for the missile swarm is deduced. 展开更多
关键词 missile swarm cooperative attack strategy collision avoidance constraint artificial potential function
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Singular optimal control of ascent stage for a surface-to-air missile
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作者 Wengui LEI Wanchun CHEN +1 位作者 Liang YANG Xiaopeng GONG 《Chinese Journal of Aeronautics》 2025年第8期527-541,共15页
This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the ty... This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the typical Goddard problem.First,the classical Legendre-Clebsch condition is applied to derive optimal conditions for the singular angle of attack,revealing that the missile turns by gravity along the singular arc.Second,the higher-order differentiation of the switching function provides the necessary conditions to determine the optimal thrust,expressed as linear functions of the costate variables.The vanishing coefficient determinant is then employed to decouple the control and costate variables,yielding the singular thrust solely dependent on state variables and identifying the singular surface.Moreover,the analytical singular control can be regarded as path constraints subject to the typical Optimal Control Problem(OCP),enabling the GPOPS-Ⅱ,a direct method framework that does not involve the singular condition,to solve the SOCP.Finally,three cases with different structures are presented to evaluate the performance of the proposed method.The results show that it takes a few steps to obtain the numerical optimal solution,which is consistent with the analytical solution derived from the calculus of variations,highlighting its great computational accuracy and effectiveness. 展开更多
关键词 Singular optimal control Optimal control problem Goddard problem Singular surface Pseudospectral method Surface-to-air missiles
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An optimal midcourse guidance method for dual pulse air-to-air missiles using linear Gauss pseudospectral model predictive control method
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作者 Jinyang WANG Wanchun CHEN +1 位作者 Liang YANG Xiaopeng GONG 《Chinese Journal of Aeronautics》 2025年第2期305-321,共17页
This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles,which is based on the framework of the linear Gauss pseudospectral model predictive control method.Firstly,a multistage optim... This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles,which is based on the framework of the linear Gauss pseudospectral model predictive control method.Firstly,a multistage optimal control problem with unspecified terminal time is formulated.Secondly,the control and terminal time update formulas are derived analytically.In contrast to previous work,the derivation process fully considers the Hamiltonian function corresponding to the unspecified terminal time,which is coupled with control,state,and costate.On the assumption of small perturbation,a special algebraic equation is provided to represent the equivalent optimal condition for the terminal time.Also,using Gauss pseudospectral collocation,error propagation dynamical equations involving the first-order correction term of the terminal time are transformed into a set of algebraic equations.Furthermore,analytical modification formulas can be derived by associating those equations and optimal conditions to eliminate terminal error and approach nonlinear optimal control.Even with their mathematical complexity,these formulas produce more accurate control and terminal time corrections and remove reliance on task-related parameters.Finally,several numerical simulations,comparisons with typical methods,and Monte Carlo simulations have been done to verify its optimality,high convergence rate,great stability and robustness. 展开更多
关键词 Optimal midcourse guidance Air-to-air missiles Gauss pseudospectral method Optimal control problem Unspecified terminal time
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Multi-platform collaborative MRC-PSO algorithm for anti-ship missile path planning
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作者 LIU Gang GUO Xinyuan +2 位作者 HUANG Dong CHEN Kezhong LI Wu 《Journal of Systems Engineering and Electronics》 2025年第2期494-509,共16页
To solve the problem of multi-platform collaborative use in anti-ship missile (ASM) path planning, this paper pro-posed multi-operator real-time constraints particle swarm opti-mization (MRC-PSO) algorithm. MRC-PSO al... To solve the problem of multi-platform collaborative use in anti-ship missile (ASM) path planning, this paper pro-posed multi-operator real-time constraints particle swarm opti-mization (MRC-PSO) algorithm. MRC-PSO algorithm utilizes a semi-rasterization environment modeling technique and inte-grates the geometric gradient law of ASMs which distinguishes itself from other collaborative path planning algorithms by fully considering the coupling between collaborative paths. Then, MRC-PSO algorithm conducts chunked stepwise recursive evo-lution of particles while incorporating circumvent, coordination, and smoothing operators which facilitates local selection opti-mization of paths, gradually reducing algorithmic space, accele-rating convergence, and enhances path cooperativity. Simula-tion experiments comparing the MRC-PSO algorithm with the PSO algorithm, genetic algorithm and operational area cluster real-time restriction (OACRR)-PSO algorithm, which demon-strate that the MRC-PSO algorithm has a faster convergence speed, and the average number of iterations is reduced by approximately 75%. It also proves that it is equally effective in resolving complex scenarios involving multiple obstacles. More-over it effectively addresses the problem of path crossing and can better satisfy the requirements of multi-platform collabora-tive path planning. The experiments are conducted in three col-laborative operation modes, namely, three-to-two, three-to-three, and four-to-two, and the outcomes demonstrate that the algorithm possesses strong universality. 展开更多
关键词 anti-ship missiles multi-platform collaborative path planning particle swarm optimization(PSO)algorithm
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Group cooperative midcourse guidance law for heterogeneous missile formation with optimal detection efficiency
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作者 Ruitao ZHANG Wenxing FU +2 位作者 Zhan CHEN Hang GUO Yangwang FANG 《Chinese Journal of Aeronautics》 2025年第10期481-506,共26页
For the problem of cooperative strike against multiple maneuvering targets,in order to improve the detection efficiency of multi-missile systems,this paper proposes a Group Cooperative Midcourse Guidance Law(GCMGL)for... For the problem of cooperative strike against multiple maneuvering targets,in order to improve the detection efficiency of multi-missile systems,this paper proposes a Group Cooperative Midcourse Guidance Law(GCMGL)for heterogeneous missile formation with optimal detection efficiency.Firstly,considering the adverse impact of target maneuvering on the guidance system,a Super-Twisting Disturbance Observer(STDO)is introduced to estimate target acceleration.Secondly,to avoid chattering in the system,a reaching law is combined with the design of the midcourse guidance law and cooperative detection control law for the leader missiles.This approach provides reference information for follower missiles and forms an optimal detection formation.Then,to achieve cooperative engagement of targets by follower missiles in groups,a group consensus protocol is introduced in the Line-of-Sight(LOS)direction to design the GCMGL.Simultaneously,in the direction normal to the LOS,when follower missiles cannot obtain the LOS angle combination information from the leader missiles,a distributed extended state observer is introduced to estimate it.Finally,a time-varying LOS angle Formation Tracking Midcourse Guidance Law(FTMGL)is designed based on this estimated information.The guidance law’s stability is validated using Lyapunov theory,and simulation experiments are performed to confirm its effectiveness and advantages. 展开更多
关键词 Heterogeneous missile formation Detection efficiency Disturbance observer Cooperative detection control law Group cooperative midcourse guidance
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Trajectory prediction algorithm of ballistic missile driven by data and knowledge
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作者 Hongyan Zang Changsheng Gao +1 位作者 Yudong Hu Wuxing Jing 《Defence Technology(防务技术)》 2025年第6期187-203,共17页
Recently, high-precision trajectory prediction of ballistic missiles in the boost phase has become a research hotspot. This paper proposes a trajectory prediction algorithm driven by data and knowledge(DKTP) to solve ... Recently, high-precision trajectory prediction of ballistic missiles in the boost phase has become a research hotspot. This paper proposes a trajectory prediction algorithm driven by data and knowledge(DKTP) to solve this problem. Firstly, the complex dynamics characteristics of ballistic missile in the boost phase are analyzed in detail. Secondly, combining the missile dynamics model with the target gravity turning model, a knowledge-driven target three-dimensional turning(T3) model is derived. Then, the BP neural network is used to train the boost phase trajectory database in typical scenarios to obtain a datadriven state parameter mapping(SPM) model. On this basis, an online trajectory prediction framework driven by data and knowledge is established. Based on the SPM model, the three-dimensional turning coefficients of the target are predicted by using the current state of the target, and the state of the target at the next moment is obtained by combining the T3 model. Finally, simulation verification is carried out under various conditions. The simulation results show that the DKTP algorithm combines the advantages of data-driven and knowledge-driven, improves the interpretability of the algorithm, reduces the uncertainty, which can achieve high-precision trajectory prediction of ballistic missile in the boost phase. 展开更多
关键词 Ballistic missile Trajectory prediction The boost phase Data and knowledge driven The BP neural network
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Is brain-inspired intelligence a new dawn for infrared imaging missile anti-interference strategies?
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作者 Shuangxi LIU Wei HUANG Xiaoqian CHEN 《Chinese Journal of Aeronautics》 2025年第5期1-4,共4页
1.Introduction Infrared Imaging Missiles(IRIMs)are advanced weapons utilizing infrared technology for target detection and tracking.Their sensors capture thermal signatures and convert them into electronic images,enab... 1.Introduction Infrared Imaging Missiles(IRIMs)are advanced weapons utilizing infrared technology for target detection and tracking.Their sensors capture thermal signatures and convert them into electronic images,enabling precise target identification and tracking.To a certain extent,the all-weather adaptability of IRIMs enables their effective operation across diverse environmental conditions,providing high targeting accuracy and cost efficiency. 展开更多
关键词 target detection infrared technology thermal signatures brain inspired intelligence infrared imaging missiles irims electronic imagesenabling precise target identification advanced weapons
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Design and Simulation of Controller for Hyper Velocity Kinetic Energy Missile 被引量:2
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作者 康长赓 雷成 刘藻珍 《Journal of Beijing Institute of Technology》 EI CAS 2000年第1期107-112,共6页
The controller design and digital simulation for the hyper velocity kinetic energy missile is investigated. A mathematical model of the trajectory deviation from the line of sight was established, the guidance closed ... The controller design and digital simulation for the hyper velocity kinetic energy missile is investigated. A mathematical model of the trajectory deviation from the line of sight was established, the guidance closed loop was compensated with a phase advance lag corrective network, a selecting algorithm of the attitude control motors used to steer the missile's attitude was presented. In the presence of a wide variety of disturbances the results of digital simulation are satisfactory to circular error probability(CEP) being less than 0 5?m. The steering scheme utilizing attitude control motors as actuators to control the attitude of the missile is feasible. 展开更多
关键词 hyper velocity missile guidance missile control attitude control motor SIMULATION
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Active Control of Initial Disturbances for Rockets and Missiles 被引量:2
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作者 毕世华 李海斌 +1 位作者 李霁红 方远 《Journal of Beijing Institute of Technology》 EI CAS 2001年第2期143-148,共6页
The active control theory and methods of initial disturbances for rockets and missiles are investigated. The rocket or missile/launcher is simplified as a flexible beam excited by a moving varying velocity rigid body ... The active control theory and methods of initial disturbances for rockets and missiles are investigated. The rocket or missile/launcher is simplified as a flexible beam excited by a moving varying velocity rigid body which has two points in contact with the beam. The control force is applied at the supporting point on the beam. Active control strategies based on optimal control theory are proposed and computer simulation is carried out. Simulation results are consistent with the theoretical results, and show that the active control strategies proposed can accomplish the purpose to control the initial disturbances actively. The results show that active control of initial disturbances for rockets and missiles is feasible for application. 展开更多
关键词 rocket or missile/launcher initial disturbances rigid body flexible beam active control
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VIRTUAL TARGET DIFFERENTIAL GAME MIDCOURSE GUIDANCE LAW FOR HYPERSONIC CRUISE MISSILE BASED ON NEURAL NETWORK 被引量:2
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作者 桑保华 姜长生 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2008年第2期121-127,共7页
For the high altitude cruising flight phase of a hypersonic cruise missile (HCM), a relative motion mod- el between the missile and the target is established by defining virtual target and combining the theory of th... For the high altitude cruising flight phase of a hypersonic cruise missile (HCM), a relative motion mod- el between the missile and the target is established by defining virtual target and combining the theory of the dif- ferential geometry with missile motion equations. Based on the model, the motion between the missile and the tar- get is considered as a single target differential game problem, and a new open-loop differential game midcourse guidance law (DGMGL) is deduced by solving the corresponding Hamiltonian Function. Meanwhile, a new struc- ture of a closed-loop DGMGL is presented and the training data for back propagation neural network (BPNN) are designed. By combining the theory of BPNN with the open-loop DGMGL obtained above, the law intelligence is realized. Finally, simulation is carried out and the validity of the law is testified. 展开更多
关键词 missiles TARGETS GUIDES back propagation neural network differential game
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Cross Spectral Estimation and Its Application in Missile Systems 被引量:1
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作者 魏华梁 刘藻珍 张天桥 《Journal of Beijing Institute of Technology》 EI CAS 1996年第1期80-84,共5页
A new method based on cross-spectrum estimation for the verification and validation of computer simulation models is expounded in accordance with the characteristics of missile systems. The new method can expose the d... A new method based on cross-spectrum estimation for the verification and validation of computer simulation models is expounded in accordance with the characteristics of missile systems. The new method can expose the differences between two time processes in several aspects and can also give quantitative analysis results about the statistical consistence between them. An application to an actual anti-tank missile system simulation is presented and the calculated results confirm the effectiveness of the method. The approach can also be employed to verify the simulation models of other dynamic systems. 展开更多
关键词 guided missile system simulation model verification cross-spectrum estimation
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Variable Structure Proportional Navigation for Homing Missile 被引量:2
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作者 宋建梅 张天桥 《Journal of Beijing Institute of Technology》 EI CAS 2000年第3期296-301,共6页
The purpose of this paper is to design control loop and guidance loop for the homing missile, to prove that the modified variable structure proportional navigation (VSPN) can be used in passive homing guidance system,... The purpose of this paper is to design control loop and guidance loop for the homing missile, to prove that the modified variable structure proportional navigation (VSPN) can be used in passive homing guidance system, and to compare the VSPN with the proportional navigation (PN). Angular rate and linear acceleration are fed back to improve the stability and robust of autopilot, VSPN and PN are compared in mathematics simulation of homing missile in attacking tanks and helicopters. The damp and the stability of the missile body are increased. The VSPN cuts down the overload of guidance phase dramatically, makes the ballistic trajectory straighter than PN and leads to smaller missdistance. The VSPN can be used for passive homing guidance system, and is especially suitable for attacking helicopter. 展开更多
关键词 homing missile variable structure proportional navigation (VSPN) proportional navigation (PN)
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Application of Generalized Predictive Adaptive Control Algorithm in the Design of Missile Control System
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作者 王正杰 李霁红 +1 位作者 张天桥 饶思成 《Journal of Beijing Institute of Technology》 EI CAS 2001年第4期356-363,共8页
To study the application of the generalized predictive adaptive control algorithm in missile control system, the algorithm is presented based on the recursive least square estimation, and a controller of the pitch c... To study the application of the generalized predictive adaptive control algorithm in missile control system, the algorithm is presented based on the recursive least square estimation, and a controller of the pitch channel of a missile is designed by using this algorithm. The simulations verify that the designed controller can meet the demands of the task well. 展开更多
关键词 generalized predictive control adaptive control ROBUSTNESS missile control system
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Simulation Study on the Feasibility of Gun-Launched Missile Against Attack Helicopters
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作者 王狂飙 张天桥 《Journal of Beijing Institute of Technology》 EI CAS 2001年第1期75-80,共6页
The feasibility of providing the tank a limited anti helicopter ability with gun launched missile is studied. A type of simulation model of gun launched missile against attack helicopters is established. The simula... The feasibility of providing the tank a limited anti helicopter ability with gun launched missile is studied. A type of simulation model of gun launched missile against attack helicopters is established. The simulation and the parameter optimization of missile control system under various circumstances are done. The gun launched missile can directly hit the helicopters in the typical tracks, all the missdistances are less than 1?m and the maximum overload is less than available overload. Gun launched missile is a feasible choice for tanks against attack helicopters. 展开更多
关键词 gun launched missile attack helicopters rolling missile beam riding guidance simulaion control system
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Missile flight simulation and attitude display
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作者 刘莉 李祖博 +1 位作者 王欢 陆真 《Journal of Measurement Science and Instrumentation》 CAS 2014年第4期5-9,共5页
Simulation has become an important method for missile flight research to reduce cost and improve accuracy. This paper concerns missile flight trajectory and attitude calculation. As a result, mechanical analysis and m... Simulation has become an important method for missile flight research to reduce cost and improve accuracy. This paper concerns missile flight trajectory and attitude calculation. As a result, mechanical analysis and modeling are done, the characteristics of missile flight decoding algorithm and attitude parameters are analyzed, the missile trajectory is dynamically simulated in a vertical plane and the missile attitude is real-time displayed. The description of missile flight process in a labo- ratory has provided a basis for actual missile flight. 展开更多
关键词 missile flight SIMULATION ATTITUDE
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Control Effect of Bio-guide Wasp Virus Missile on Ostrinia furnacalis and Its Benefits for Maize Production in Nanchong City
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作者 彭昌家 白体坤 +8 位作者 丁攀 冯礼斌 尹怀中 龙维国 杨宇衡 杨建华 何海燕 苟建华 罗怀海 《Agricultural Science & Technology》 CAS 2016年第3期662-666,共5页
In order to promote "green plant protection", reduce the administration dosage and residue of pesticides and control cost of environment pollution, and improve maize production, quality and agricultural ecological e... In order to promote "green plant protection", reduce the administration dosage and residue of pesticides and control cost of environment pollution, and improve maize production, quality and agricultural ecological environment safety. In this study, the control effect and benefit of bio-guide wasp virus missile(BGWVM) on Ostrinia furnacalis in Nanchong City was investigated by using insect light traps and combined method of field investigation and experimental demonstration. According to the results, applying 30-37 pairs of BGWVM per hectare exhibited an average control efficiency of 78.0%, and the control cost was 139.50-172.50 CNY/hm2, which was reduced by 142.50-168.00 CNY/hm^2 compared with conventional chemical control. Average maize yield in BGWVM demonstration plot was 817.8 kg/hm2 higher and improved by 11.0% compared with blank control plot. The output value was improved by 1 799.16 CNY/hm^2 and the revenue increased by 1 941.66-1 967.16CNY/hm2. During 2003-2014, the cumulative demonstration and popularization area of BGWVM technique in Nanchong City had reached 24 507.33 hm^2, and the cumulative yield increment reached 20.042 1 million kg. BGWVM application improved total output value by 44.092 6 million CNY and saved control cost by 3.492 3-4.117 2 million CNY, thus increasing the revenue by 47.584 9-48.209 8 million CNY. BGWVM application reduced 551.41 t of 5% dimehypo GG or 12.87 t of 90%monosultap WP. In addition, BGWVM technique is simple to use, labor-saving and safe for human, animals, environment and crops, with significant economic, ecological and social benefits and without any side effect, which has become an ideal substitute for controlling O. furnacalis and reducing chemical pesticides in organic agriculture industry, modern agriculture industry, production of green and pollution-free agricultural products and IBM prevention and control demonstration gardens. 展开更多
关键词 Ostrinia furnacalis Bio-guide wasp virus missile Prevention and control Effect BENEFIT Evaluation
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Bayes Estimation of Parameter for the Safety Component Failure Model of the Safe Arming System of Missile
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作者 陈放 高培旺 马晓青 《Journal of Beijing Institute of Technology》 EI CAS 2000年第3期283-286,共4页
A Bayesian method is used to evaluate the component safety failure model parameter of the safe arming system of an air faced missile in flight. It was proved that Bayes estimation of the model parameter is coinciden... A Bayesian method is used to evaluate the component safety failure model parameter of the safe arming system of an air faced missile in flight. It was proved that Bayes estimation of the model parameter is coincident with the physical explanation of the prior probability density distribution of the random parameter. 展开更多
关键词 safe arming system of air faced missile safety component Bayes estimation
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